This invention relates generally to finite element modeling and more particularly concerns a method and apparatus for generating finite element meshes from computed tomography (CT) data.
The generation of the finite element mesh continues to be the bane of the analyst and the principle bottleneck in the finite element modeling process. This problem is becoming somewhat ameliorated with the introduction of fully automatic mesh generators. Despite progress, commercial systems still lack robustness and have serious limitations, especially for geometrically complex industrial components. Conventional approaches to automatic meshing of a continuum require a solid model; i.e., a geometric representation that can ascertain if a point in space is inside, outside, or on the object. Unfortunately, a priori solid models are not always available for purposes of meshing. The most apparent reason for this is that computer-aided design (CAD) and computer-aided engineering (CAE) are not well integrated. Furthermore, wireframe and surface modeling technology still dominates CAD systems. Thus, there is typically a need to create a solid model as part of the CAE process. Several classical methods generate solid models, including top-down constructive solid geometry (CSG) and boundary representation (B-rep) approaches, as well as, bottom-up construction of areas and volumes.
Even in the presence of a solid model there are still barriers that must be overcome. First, the as-manufactured part may not be the same as the as-designed definition. This may be because of manufacturing tolerances in the system, material shrinkage, or part warpage caused by residual stresses. Thus, when analysis is performed on the designed part, the physical part dimensions may be sufficiently different that the analysis is suspect. Second, although analysis is ideally a scheduled task within the design/analysis process, before manufacturing or test, this is not always the case. In many instances, analysis is not performed at all, requisite 3-D analysis is so long that the component may have already been manufactured before the results of the analysis are known. Third, if a field failure does occur, then analysis of the failed component is mandated. Nominal dimensions may not suffice here. These scenarios point to a dramatic need for rapid turn around of analysis of the physical component.
Computed tomography (CT) is a technology that offers much promise in helping to address many of the above issues. This technology has been extensively used for medical diagnostics and for x-ray inspection of industrial components. Early applications of CT technology concentrated on creating images of three dimensional surfaces contained with the scanned cross-sectional or slice volume of the patient or part. Initial approaches created contours of material boundaries one slice at a time. Using the contours from adjacent slices, algorithms stitched the contours together to form triangular surfaces. These contour-based algorithms could not reliably and automatically handle adjacent slices that contained different numbers of contours.